Abstract
In this paper, we study the improved perturbed nonlinear Schrödinger equation with cubic quadratic nonlinearity (IPNLSE-CQN) to describe the propagation properties of nonlinear periodic waves (PW) in fiber optics. We obtain the chirped periodic waves (CPW) with some Jacobi elliptic functions (JEF) and also obtain some solitary waves (SW) such as dark, bright, hyperbolic, singular and periodic solitons. The nonlinear chirp associated with each of these optical solitons was observed to be dependent on the pulse intensity. The graphical behavior of these waves will also be displayed.
Highlights
Perturbed Nonlinear SchrödingerA chirp is a signal whose frequency changes over time
The NLSE is used to describe these pulses, and it only includes the effects of group velocity dispersion (GVD) and self-phase modulation that are valid in the picosecond region
We studied the IPNLSECQN in order to obtain some chirped periodic and soliton waves
Summary
A chirp is a signal whose frequency changes over time. The chirping sound generated by birds is the source of the term chirp. The propagation of chirped soliton pulses in fiber optics is getting popular due to a wide range of applications in amplification and pulse compression. Higher-order effects such as self-steeping (SS), self-frequency (SF) shift, and quintic nonlinearity can occur when optical pulses are short (in the femtosecond region). Vysa et al studied the NLSE with SS and SF shift effect in order to obtain the chirped chiral solitons [19]. For a higher-order NLSE with competing cubic-quintic-septic nonlinearities, non-Kerr quintic nonlinearity, SS, and SF shift, Bouzida et al obtained families of chirped soliton-like solutions. It was demonstrated that there are exact chirped soliton solutions for the generalised NLSE with polynomial nonlinearity and non-Kerr terms of arbitrary order [21].
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